Table of Contents
Topic
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Page #
6.6A Absolute Value Less ThAND
6.6B Absolute Value GreatOR Than
6.7 Two Variable Inequalities
7.1 Solve Systems By Graphing
7.2 Solve Systems By Substitution
7.3 Solve Systems By Combination
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Solve Systems by Substitution:
1) Line up the x and y values in standard
form
2) Make one variable opposite each other if
needed
3) Add the equations
4) Solve for the variable
5) Plug answer into any equation to find
the other variable
6) Write answer as ordered pair (x,y)
Example 1: Rewrite the linear system so that the
like terms are arranged in columns
a.
3x – y = 23
y + 8x = 11
3x – y = 23
8x + y = 11
Example 1: Rewrite the linear system so that the
like terms are arranged in columns
b.
4x = y + 1
3y + 4x = 7
4x – y = 1
4x + 3y = 7
Example 1: Rewrite the linear system so that the
like terms are arranged in columns
c.
7x – y = 13
y = 14x - 3
7x – y = 13
-14x + y = -3
Example 2: Use the linear combination method to
solve the system.
+
2x + 3y = 11
-2x + 5y = 13
8y = 24
y=3
2x + 3(3) = 11
2x + 9 = 11
2x = 2
x=1
(1, 3)
ans:_______________
+
6x – 4y = 14
-3x + 4y = 1
3x
= 15
x=5
-3(5) + 4y = 1
-15 + 4y = 1
4y = 16
y=4
(5, 4)
ans:_______________
+
4x – 3y = 5
–2x + 3y = -7
2x
= -2
x = -1
-2(-1) + 3y = -7
2 + 3y = -7
3y = -9
y = -3
(-1, -3)
ans:_______________
Example 3: Use the linear combination method to solve the
system.
3x + 4y = -6
2y = 3x +6
3x + 4y = -6
+ -3x + 2y = 6
6y = 0
y=0
3x + 4(0) = -6
3x = -6
x = -2
(-2, 0)
ans:_______________
8x – 4y = -4
4y = 3x + 14
8x – 4y = -4
+ -3x + 4y = 14
5x
= 10
x=2
-3(2) + 4y = 14
-6 + 4y = 14
4y = 20
y=5
(2, 5)
ans:_______________
-5y = -4x – 6
2x + 5y = 12
+
4x – 5y = –6
2x + 5y = 12
6x
=6
x=1
2(1) + 5y = 12
2 + 5y = 12
5y = 10
y=2
(1, 2)
ans:_______________